palindrome_power_palindrome.ipynb

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     "text": [
      "101^2 = 10201\n",
      "101^3 = 1030301\n",
      "101^4 = 104060401\n",
      "202^2 = 40804\n",
      "212^2 = 44944\n",
      "121^2 = 14641\n",
      "1001^2 = 1002001\n",
      "1001^3 = 1003003001\n",
      "1001^4 = 1004006004001\n",
      "2002^2 = 4008004\n",
      "10001^2 = 100020001\n",
      "10001^3 = 1000300030001\n",
      "10001^4 = 10004000600040001\n",
      "20002^2 = 400080004\n",
      "11011^2 = 121242121\n",
      "11011^3 = 1334996994331\n",
      "10101^2 = 102030201\n",
      "10101^3 = 1030607060301\n",
      "20102^2 = 404090404\n",
      "10201^2 = 104060401\n",
      "11211^2 = 125686521\n"
     ]
    }
   ],
   "source": [
    "def palindromes():\n",
    "    ps = [[]]+[[x] for x in range(0,10)]\n",
    "    for p in ps:\n",
    "        yield pint(p)\n",
    "    while True:\n",
    "        nps = []\n",
    "        for p in ps:\n",
    "            for i in range(0,10):\n",
    "                np = [i]+p+[i]\n",
    "                if i>0:\n",
    "                    yield pint(np)\n",
    "                nps.append(np)\n",
    "        ps = nps\n",
    "\n",
    "def pint(p):\n",
    "    t = 0\n",
    "    for x in p:\n",
    "        t = 10*t + x\n",
    "    return t\n",
    "        \n",
    "def is_palindrome(s):\n",
    "    return s[::-1]==s\n",
    "    \n",
    "def is_repdigit(s):\n",
    "    return len(set(s))==1\n",
    "    \n",
    "for p,_ in zip(palindromes(),range(1000)):\n",
    "    if p>10 and not is_repdigit(str(p)):\n",
    "        for i in range(2,10):\n",
    "            q = p**i\n",
    "            if is_palindrome(str(q)):\n",
    "                print('{}^{} = {}'.format(p,i,q))"
   ]
  }
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